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Novel hybrid evolutionary algorithm for bi-objective optimization problems.

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This study introduces a novel three-Phase Hybrid Evolutionary Algorithm (3PHEA) to solve the Bi-objective Traveling Salesman Problem (BTSP). The new method significantly outperforms existing approaches, finding up to 80% of optimal trade-off solutions.

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Area of Science:

  • Operations Research
  • Computer Science
  • Optimization

Background:

  • The Bi-objective Traveling Salesman Problem (BTSP) involves minimizing conflicting objectives like travel time and cost.
  • Finding optimal trade-off solutions (Pareto fronts) is crucial but computationally challenging.

Purpose of the Study:

  • To develop and evaluate a novel algorithm for solving the BTSP.
  • To compute and analyze the trade-off solutions between travel time and monetary cost.

Main Methods:

  • Introduction of a three-Phase Hybrid Evolutionary Algorithm (3PHEA).
  • 3PHEA integrates the Lin-Kernighan Heuristic, an improved Non-Dominated Sorting Genetic Algorithm, and Pareto Variable Neighborhood Search.
  • Comparative analysis against three existing BTSP algorithms using 20 benchmark instances (100-1000 cities).

Main Results:

  • The proposed 3PHEA demonstrated significant superiority over existing methods.
  • 3PHEA achieved coverage of up to 80% of the true Pareto fronts.
  • Performance was assessed using multiple multi-objective indicators including hypervolume and generational distance.

Conclusions:

  • The novel 3PHEA is a highly effective approach for solving the Bi-objective Traveling Salesman Problem.
  • The algorithm provides superior performance in finding optimal trade-off solutions compared to current methods.